Any good ones not too far from the Vatican?
If you are only getting young wine, Enoteca Contantini in Piazza Cavour is nice. I caveat the young wine because when I was there in 2003, the cellar was hot, not just warm (record breaking heat wave). If they have put in air con in their cellar, then just don’t buy wine from before it was installed.
If you want to buy from a store with great storage, Trimani. But it’s the opposite end of town, further east than the Via Veneto.